Proof Index
01-vector-definition-algebraic-definition |
01-vector-definition-column-vector-is-the-standard-representation |
01-vector-definition-equality-of-vectors |
01-vector-definition-geometric-definition |
01-vector-definition-is-invariant-under-coordinate-transformation |
01-vector-definition-properties-of-transpose |
01-vector-definition-transpose-of-a-vector |
01-vector-definition-vector-versus-coordinate |
02-systems-of-linear-equations-definition-algebraic-form |
02-systems-of-linear-equations-point-vs-position-vector |
02-vector-operation-scalar-vector-multiplication-algebraic-definition |
02-vector-operation-vector-addition-algebraic-definition |
02-vector-operation-vector-addition-example |
02-vector-operation-vector-subtraction-example |
03-vector-norm-distance |
03-vector-norm-l1-norm |
03-vector-norm-l2-norm |
03-vector-norm-lp-norm |
03-vector-norm-norm-on-a-vector-space |
2dparameters |
875-koko-eating-bananas-binary-search-pseudocode |
875-koko-eating-bananas-externally-derived-constraints |
875-koko-eating-bananas-feasibility-function |
875-koko-eating-bananas-feasibility-function-for-koko-eating-bananas |
875-koko-eating-bananas-monotonicity |
875-koko-eating-bananas-why-ceiling |
accuracy-definition |
accuracy-remark |
alg:em-gmm-1 |
alg:gmm-sampling |
amortized-time-complexity |
axiom:additivity |
axiom:non-negativity |
axiom:normalization |
binary-search-mathematical-representation |
binary-search-mathematical-representation-iterative |
binary-search-pseudocode-iterative |
binary-search-pseudocode-recursive |
binary-search-remark-what-if-we-want-to-find-39 |
brute-force-search-kmeans |
categorical-distribution |
categorical-distribution-example |
categorical-distribution-gmm |
categorical-multinomial-distribution |
categorical-multinomial-distribution-gmm |
cicd-concept-pinning-pylint |
conditional-independence |
cor:law-total-probability |
cor:moment_generating_function_sum_of_N_rv |
cor_continuous_expectation |
cor_iid_joint_pdf |
cor_probability_interval |
cor_standard_gaussian |
corollary:chebyshev-iid |
corollary:inclusion-exclusion |
corollary:inequality-bounds |
corollary:law_of_iterated_expectation |
corollary:positive_definite_matrix |
corollary:probability-of-complements |
corollary:probability-of-empty-set |
cosine-similarity-definition |
criterion:kmeans-optimal-assignment |
criterion:kmeans-optimal-cluster-centers |
dataset-definition |
decoder-concept-attention-exact-match-scenario |
decoder-concept-attention-scores |
decoder-concept-attention-scoring-function |
decoder-concept-attention-scoring-function-with-scaling |
decoder-concept-attention-scoring-function-with-scaling-softmax |
decoder-concept-context-vector-matrix |
decoder-concept-gradient-saturation |
decoder-concept-linear-projections-queries-keys-values |
decoder-concept-linear-projections-queries-keys-values-remark |
decoder-concept-numerical-stability |
decoder-concept-query-key-iid |
decoder-concept-scaled-dot-product-attention |
decoder-concept-softmax-normalization-attention-weights |
decoder-concept-variance-dot-product |
decoder-layer-normalization |
decoder-positional-encoding |
decoder-simplified-objective-function |
def-conditional-likelihood-function-linear-regression |
def-conditional-log-likelihood-function-linear-regression |
def-cove-process |
def-empirical-risk |
def-gelu |
def-gelu-notation |
def-generalization-gap |
def-hallucination |
def-loss-function |
def-loss-function-rv |
def-marginal-pmf-pdf |
def-positionwise-ffn |
def-positionwise-ffn-notation |
def-r-squared |
def-sample-average |
def-true-risk |
def-voronoi-region |
def:assignment |
def:bayes-theorem |
def:bernoulli_trials_1 |
def:bernoulli_trials_2 |
def:binomial_as_sum_of_bernoulli |
def:centroids |
def:characteristic_polynomial |
def:conditional-cdf-of-a-continuous-random-variable |
def:conditional-cdf-of-a-discrete-random-variable |
def:conditional-independence |
def:conditional-likelihood-machine-learning |
def:conditional-pdf-of-a-continuous-random-variable |
def:conditional-pmf |
def:conditional-variance |
def:conditional_expectation |
def:contour_lines |
def:contour_map |
def:correlation_coefficient |
def:cosine_dot_product |
def:covariance |
def:covariance-matrix |
def:covariance_matrix_2d |
def:decision_boundary |
def:diagonalizable_matrix |
def:dichotomy |
def:disjoint |
def:eigendecomposition |
def:eigenvalue |
def:expectation-random-vector |
def:geo |
def:independence |
def:independence-conditional |
def:independent-events |
def:independent-random-vector |
def:joint-cdf-random-vector |
def:joint-expectation-independent-random-vector |
def:joint_expectation |
def:kmeans-cost |
def:kmeans-loss |
def:kmeans-objective |
def:kmeans-voronoi-partition |
def:likelihood |
def:likelihood-iid |
def:likelihood-iid-higher-dim |
def:likelihood-iid-supervised-learning |
def:limiting-perspective |
def:log-likelihood |
def:marginal-pdf-random-vector |
def:matrix_representation_of_a_eigenvalue_and_eigenvector |
def:maximum-likelihood-estimation |
def:maximum-likelihood-estimation-for-bernoulli-distribution |
def:moment_generating_function |
def:multivariate_gaussian |
def:multivariate_gaussian_distribution_2d |
def:naive-bayes-likelihood |
def:naive-bayes-log-likelihood |
def:naive-bayes-max-feature-params |
def:naive-bayes-max-priors |
def:pdf-independent-random-vector |
def:pdf-random-vector |
def:poi |
def:positive_definite |
def:positive_semi_definite |
def:random-vector |
def:state_space_binomial |
def_bernoulli_distribution_cdf |
def_bernoulli_distribution_pmf |
def_binomial_distribution_cdf |
def_binomial_distribution_pmf |
def_cdf |
def_continuous_cdf |
def_continuous_cdf_continuity |
def_continuous_expectation |
def_continuous_random_variable |
def_continuous_uniform_distribution_cdf |
def_continuous_uniform_distribution_pdf |
def_countable_set |
def_discrete_expectation |
def_discrete_random_variables |
def_discrete_uniform_cdf |
def_discrete_uniform_pmf |
def_error_function |
def_exponential_distribution_cdf |
def_exponential_distribution_pdf |
def_gaussian_distribution_cdf |
def_gaussian_distribution_pdf |
def_iid |
def_iid_N |
def_iid_restated |
def_independent |
def_independent_n |
def_joint_cdf |
def_joint_cdf_cont |
def_joint_pdf |
def_joint_pmf |
def_moments |
def_moments_continuous |
def_pmf |
def_probability_density_function |
def_probability_density_function_1d |
def_standard_deviation |
def_standard_gaussian_distribution |
def_standard_normal_distribution_cdf |
def_state_space |
def_uncountable_set |
def_variance |
def_variance_alt |
def_variance_continuous |
def_variance_continuous_alt |
def_zero_measure |
definition-0 |
definition-2 |
definition:convex |
dir-deriv-theorem |
directional_derivative_example |
ece595_def4.6 |
elbow-method |
event |
event_space |
ex:gmm-update-mixture-weights |
ex:log-likelihood-bernoulli |
ex:moment_generating_function_1 |
ex:moment_generating_function_2 |
ex:moment_generating_function_bernoulli |
ex:poi |
ex:poi2 |
ex:two-coins |
ex_gaussian_iid |
ex_gaussian_iid_cont |
ex_iid_1 |
example-4 |
example-bayes-optimal-classifier |
example-empirical-risk |
example-gmm-initialization |
example-marginal-pdf-bivariate-normal |
example-naive-bayes-feature-1-class-2 |
example-pixels |
example:assignment |
example:conditional-independence |
example_cdf |
example_growth_function |
example_pmf_coin_toss |
example_pmf_two_dice_rolls |
example_random_variable_coin_toss |
example_random_variable_dice_roll |
example_state_space_coin_toss |
example_state_space_dice_roll |
example_variable_vs_random_variable |
experiment |
fundamental_theorem_of_calculus |
fundamental_theorem_of_calculus_corollary |
gd-algo |
gpt-notations-one-hot-example |
gpt-notations-one-hot-example-dup |
grad_vec |
how-does-softmax-work-additivity |
how-does-softmax-work-non-negativity |
how-does-softmax-work-normalization |
iid-assumption |
jacobian-softmax |
joint-and-conditional-probability |
joint-distribution-example |
kmeans-monotonic-decrease |
lagrangian-method |
lemma-hallucination-factors |
lemma:hoeffding |
likelihood |
linear-algebra-01-preliminaries-field |
linear-algebra-02-vectors-04-vector-products-dot-product-example-1 |
linear-algebra-preliminaries-fields-on-the-real-numbers |
linear-search-loop-invariant-theorem |
lloyd-kmeans-algorithm |
marginal-distribution-and-normalization-constant |
master-theorem-generic-divide-and-conquer-algorithm |
matrix-formulation-softmax |
measure_zero_sets |
ml-lifecycle-02-ranking-items-newsfeed |
ml-lifecycle-032-normalization |
monotone-convergence |
naive-bayes-inference-algorithm |
notation-overload |
obs-complexity |
omniverse-dsa-searching-algorithms-binary-search-recursive-algorithm-correctness |
parameter-vector |
posterior |
pre_image |
prf-example-conditional-expectation |
prf-example-learner |
prf-gmm-update-covariance-example |
prf-gmm-update-means-example |
prf-remark-iid |
prf-remark-notation-convention-linear-regression |
prf-remark-x-random |
prf:algorithm-label-binarize |
prf:definition |
prf:definition-f1 |
prf:definition-fnr |
prf:definition-fpr |
prf:definition-recall |
prf:definition-specificity |
prf:definition:in-sample-error |
prf:definition:out-sample-error |
prf:definition:zero-one-loss |
prf:example-bernoulli-parameter |
prf:example-bits |
prf:example-f1 |
prf:example-gaussian-parameter |
prf:example-gmm-1 |
prf:example-multiclass-benign |
prf:example-multiclass-borderline |
prf:example-multiclass-malignant |
prf:example-precision |
prf:example-recall |
prf:naive-bayes-estimation-algorithm |
prf:remark-bias |
prf:remark-bounding-the-entire-hypothesis-set |
prf:remark-gmm-closed-form |
prf:remark-major-confusion-alert |
prf:remark-notation-gmm |
prf:remark:kmeans-optimal-cluster-centers-notation |
prf:remark:why_contours_of_multivariate_gaussian_are_elliptical |
prior |
probability-theory-central-moments |
probability-theory-mean-from-cdf |
probability-theory-mean-from-cdf-x-gt-0 |
probability-theory-mean-from-cdf-x-lt-0 |
probability-theory-median |
probability-theory-median-from-cdf |
probability-theory-mode |
probability_law |
prop:bernoulli |
prop:bernoulli_var |
prop:bino_exp |
prop:bino_var |
prop:conditional-probability-equalities |
prop:correlation_coefficient |
prop:covariance |
prop:geo_exp |
prop:geo_var |
prop:mean_vector_covariance_matrix |
prop:poi_exp |
prop:poi_var |
prop_continuous_cdf_interval |
prop_continuous_discrete_cdf |
prop_dc_shift |
prop_expectation_dc_shift_continuous |
prop_expectation_dc_shift_discrete |
prop_expectation_function_continuous |
prop_expectation_function_discrete |
prop_expectation_linearity_continuous |
prop_expectation_linearity_discrete |
prop_expectation_scaling_continuous |
prop_expectation_scaling_discrete |
prop_expectation_stronger_linearity_continuous |
prop_expectation_stronger_linearity_discrete |
prop_linearity |
prop_scaling |
prop_sum_poi |
random_variables |
rem-erm-trial-and-error |
rem-iid-erm |
rem-risk-vs-loss |
rem:gmm-update-mixture-weights-depends-on-all-parameters |
rem:likelihood |
rem:where-y |
rem_exponential_distribution_pdf |
rem_iid |
rem_open_equals_closed_interval |
rem_probability_density_function |
remark-0 |
remark-4 |
remark-6 |
remark-approx-gelu |
remark-approx-gelu-notation |
remark-bayes-optimal-classifier |
remark-bayes-optimal-classifier-naive-bayes |
remark-empirical-parameters |
remark-finding-cdf-is-easier |
remark-gmm-update-means |
remark-interpretation-true-risk |
remark-joint-pdf |
remark-joint-pmf |
remark-kmeans-greedy |
remark-kmeans-problem-statement |
remark-learning-problem-notations |
remark-learning-problem-notations-learning-theory |
remark-likelihood-function-notation-clash |
remark-marginal-distribution-ltp |
remark-notation |
remark-random-variable-is-a-function |
remark-summary-1 |
remark-things-to-note |
remark-univariate-mle |
remark-what-is-a-joint-distribution |
remark:cauchy_schwarz |
remark:conditional-distribution-is-a-distribution-for-a-sub-population |
remark:conditional-expectation-is-the-expectation-for-a-sub-population |
remark:conditional-pmf |
remark:convex_concave |
remark:cost-function-is-a-function-of-assignment-and-centroids |
remark:iid_assumption |
remark:kmeans-cost-function-is-a-function-of-assignments-and-cluster-centers |
remark:union_bound_tightness |
remove-duplicates-from-sorted-array-two-pointers-algorithm-1 |
remove-duplicates-from-sorted-array-two-pointers-algorithm-2 |
remove-duplicates-from-sorted-array-two-pointers-claim |
restricted_hypothesis_space |
rmk:infinite-hypothesis-space |
rmk:maximum-likelihood-estimation |
rmk:random-vector |
rmk_continuous_uniform_distribution |
rmk_gaussian_distribution_pdf |
sample_complexity_example |
sample_space |
sauer's_lemma |
shatters |
softmax-output-vector |
software-engineering-concurrency-parallelism-asynchronous-generator-yield-is-an-expression |
software-engineering-concurrency-parallelism-asynchronous-generator-yield-remark |
some-remarks |
stack-list-amortized-worst-case-time-complexity |
stack-list-remarks |
stirling-numbers |
term-document-example-info-retrieval |
term-document-remark |
theorem-3 |
theorem-empirical-risk-minimization |
theorem-erm-approximates-trm |
theorem-expectation-of-sample-average |
theorem-gmm-update-covariance |
theorem-gmm-update-means |
theorem-hoeffding-inequality-restated |
theorem-learning-theory-1 |
theorem-strong-law-of-large-numbers |
theorem-true-risk-minimization |
theorem-variance-of-sample-average |
theorem-weak-law-of-large-numbers |
theorem-weak-law-of-large-numbers-restated |
theorem:cauchy_schwarz |
theorem:chebyshev |
theorem:chernoff-bound |
theorem:convolutions-of-random-variables |
theorem:hoeffding |
theorem:jensen |
theorem:law_of_total_expectation |
theorem:markov |
theorem:method-of-transformations |
theorem:positive_semi_definite_covariance_matrix |
theorem:positive_semi_definite_matrix |
theorem:sum-of-common-distributions |
theorem:sum-of-gaussian-random-variables |
theorem:sum-of-poisson-random-variables |
theorem:union_bound |
thm:cauchy_schwarz_inequality |
thm:conditional-pdf-of-an-event-given-y |
thm:conditional-pmf-of-an-event-a-given-y |
thm:covariance |
thm:covariance-matrix-independent |
thm:disjoint-vs-independent |
thm:eigenvalues_are_roots_of_the_characteristic_polynomial |
thm:eigenvalues_of_a_symmetric_matrix |
thm:empirical_correlation_coefficient |
thm:equivalent_conditions_for_lambda_to_be_an_eigenvalue |
thm:generalization-bound |
thm:gmm-update-mixture-weights |
thm:independence_and_covariance |
thm:independence_and_joint_expectation |
thm:law-total-probability |
thm:linear_transformation_mean_covariance |
thm:linearity_of_covariance |
thm:minimizing-individual-clusters-cost-is-equivalent-to-minimizing-the-objective-function |
thm:moment_generating_function_properties |
thm:moment_generating_function_sum_of_2_rv |
thm:moment_generating_function_sum_of_gaussian_rv |
thm:moment_generating_function_sum_of_poisson_rv |
thm:orthornormal_basis |
thm:poi_bin |
thm:shifting_mean_covariance |
thm_cdf |
thm_cdf_arbitrary_gaussian_distribution |
thm_cdf_point |
thm_cdf_right_continuous |
thm_continuous_uniform_distribution |
thm_existence_of_expectation_continuous |
thm_existence_of_expectation_discrete |
thm_exponential_distribution_expectation_variance |
thm_joint_pmf_pdf |
thm_linear_transformation_gaussian_distribution |
thm_pdf_derivative_cdf |
thm_pmf_cdf |
thm_pmf_normalization |
time-complexity |
two-pointers-technique-algorithm |
two-pointers-technique-meet-in-middle-algorithm |
two-sum-167-two-sum-ii-input-array-is-sorted-two-pointers-algorithm |
two-sum-167-two-sum-ii-input-array-is-sorted-two-pointers-claim |
two-sum-time-complexity-nested-loops-avg-case |
type-theory-01-subtypes-definition-nominal-structural |
type-theory-01-subtypes-definition-subtype |
type-theory-01-subtypes-example-int-type-as-set |
type-theory-01-subtypes-remark-coercive-conversion |
type-theory-04-generics-definition-type-constructor |
type-theory-04-generics-remark-no-automatic-lifting |
type-theory-06-variance-function-subtyping |
type-theory-liskov-substitution-principle |
type-theory-subtype-and-type-safety |
type-theory-subtype-criterion |
underlying-distributions |
unordered-linear-search-mathematical-representation-iterative |
unordered-linear-search-pseudocode-iterative |
valid-parentheses-using-stack |
vc_dimension |
vc_dimension_of_a_2d_perceptron |
vc_dimension_of_a_perceptron |
vc_generalization_bound |
why-do-we-use-warmup-cosine-scheduler-definition |
why-do-we-use-warmup-cosine-scheduler-definition-duplicate |
worst-case-only
| 01-vector-definition-algebraic-definition | ||
01-vector-definition-algebraic-definition (linear_algebra/02_vectors/01-vector-definition) | definition | |
| 01-vector-definition-column-vector-is-the-standard-representation | ||
01-vector-definition-column-vector-is-the-standard-representation (linear_algebra/02_vectors/01-vector-definition) | remark | |
| 01-vector-definition-equality-of-vectors | ||
01-vector-definition-equality-of-vectors (linear_algebra/02_vectors/01-vector-definition) | definition | |
| 01-vector-definition-geometric-definition | ||
01-vector-definition-geometric-definition (linear_algebra/02_vectors/01-vector-definition) | definition | |
| 01-vector-definition-is-invariant-under-coordinate-transformation | ||
01-vector-definition-is-invariant-under-coordinate-transformation (linear_algebra/02_vectors/01-vector-definition) | theorem | |
| 01-vector-definition-properties-of-transpose | ||
01-vector-definition-properties-of-transpose (linear_algebra/02_vectors/01-vector-definition) | property | |
| 01-vector-definition-transpose-of-a-vector | ||
01-vector-definition-transpose-of-a-vector (linear_algebra/02_vectors/01-vector-definition) | definition | |
| 01-vector-definition-vector-versus-coordinate | ||
01-vector-definition-vector-versus-coordinate (linear_algebra/02_vectors/01-vector-definition) | example | |
| 02-systems-of-linear-equations-definition-algebraic-form | ||
02-systems-of-linear-equations-definition-algebraic-form (linear_algebra/01_preliminaries/02-systems-of-linear-equations) | definition | |
| 02-systems-of-linear-equations-point-vs-position-vector | ||
02-systems-of-linear-equations-point-vs-position-vector (linear_algebra/01_preliminaries/02-systems-of-linear-equations) | remark | |
| 02-vector-operation-scalar-vector-multiplication-algebraic-definition | ||
02-vector-operation-scalar-vector-multiplication-algebraic-definition (linear_algebra/02_vectors/02-vector-operation) | definition | |
| 02-vector-operation-vector-addition-algebraic-definition | ||
02-vector-operation-vector-addition-algebraic-definition (linear_algebra/02_vectors/02-vector-operation) | definition | |
| 02-vector-operation-vector-addition-example | ||
02-vector-operation-vector-addition-example (linear_algebra/02_vectors/02-vector-operation) | example | |
| 02-vector-operation-vector-subtraction-example | ||
02-vector-operation-vector-subtraction-example (linear_algebra/02_vectors/02-vector-operation) | example | |
| 03-vector-norm-distance | ||
03-vector-norm-distance (linear_algebra/02_vectors/03-vector-norm) | definition | |
| 03-vector-norm-l1-norm | ||
03-vector-norm-l1-norm (linear_algebra/02_vectors/03-vector-norm) | definition | |
| 03-vector-norm-l2-norm | ||
03-vector-norm-l2-norm (linear_algebra/02_vectors/03-vector-norm) | definition | |
| 03-vector-norm-lp-norm | ||
03-vector-norm-lp-norm (linear_algebra/02_vectors/03-vector-norm) | definition | |
| 03-vector-norm-norm-on-a-vector-space | ||
03-vector-norm-norm-on-a-vector-space (linear_algebra/02_vectors/03-vector-norm) | definition | |
| 2dparameters | ||
2dparameters (influential/naive_bayes/02_concept) | remark | |
| 875-koko-eating-bananas-binary-search-pseudocode | ||
875-koko-eating-bananas-binary-search-pseudocode (dsa/searching_algorithms/binary_search/problems/875-koko-eating-bananas) | algorithm | |
| 875-koko-eating-bananas-externally-derived-constraints | ||
875-koko-eating-bananas-externally-derived-constraints (dsa/searching_algorithms/binary_search/problems/875-koko-eating-bananas) | remark | |
| 875-koko-eating-bananas-feasibility-function | ||
875-koko-eating-bananas-feasibility-function (dsa/searching_algorithms/binary_search/problems/875-koko-eating-bananas) | definition | |
| 875-koko-eating-bananas-feasibility-function-for-koko-eating-bananas | ||
875-koko-eating-bananas-feasibility-function-for-koko-eating-bananas (dsa/searching_algorithms/binary_search/problems/875-koko-eating-bananas) | definition | |
| 875-koko-eating-bananas-monotonicity | ||
875-koko-eating-bananas-monotonicity (dsa/searching_algorithms/binary_search/problems/875-koko-eating-bananas) | definition | |
| 875-koko-eating-bananas-why-ceiling | ||
875-koko-eating-bananas-why-ceiling (dsa/searching_algorithms/binary_search/problems/875-koko-eating-bananas) | remark | |
| accuracy-definition | ||
accuracy-definition (influential/evaluation_metrics/classification/accuracy) | definition | |
| accuracy-remark | ||
accuracy-remark (influential/evaluation_metrics/classification/accuracy) | remark | |
| alg:em-gmm-1 | ||
alg:em-gmm-1 (influential/gaussian_mixture_models/02_concept) | algorithm | |
| alg:gmm-sampling | ||
alg:gmm-sampling (influential/gaussian_mixture_models/02_concept) | algorithm | |
| amortized-time-complexity | ||
amortized-time-complexity (dsa/stack/questions/232-implement-queue-using-stacks) | example | |
| axiom:additivity | ||
axiom:additivity (probability_theory/02_probability/0203_probability_axioms) | axiom | |
| axiom:non-negativity | ||
axiom:non-negativity (probability_theory/02_probability/0203_probability_axioms) | axiom | |
| axiom:normalization | ||
axiom:normalization (probability_theory/02_probability/0203_probability_axioms) | axiom | |
| binary-search-mathematical-representation | ||
binary-search-mathematical-representation (dsa/searching_algorithms/binary_search/concept) | algorithm | |
| binary-search-mathematical-representation-iterative | ||
binary-search-mathematical-representation-iterative (dsa/searching_algorithms/binary_search/concept) | algorithm | |
| binary-search-pseudocode-iterative | ||
binary-search-pseudocode-iterative (dsa/searching_algorithms/binary_search/concept) | algorithm | |
| binary-search-pseudocode-recursive | ||
binary-search-pseudocode-recursive (dsa/searching_algorithms/binary_search/concept) | algorithm | |
| binary-search-remark-what-if-we-want-to-find-39 | ||
binary-search-remark-what-if-we-want-to-find-39 (dsa/searching_algorithms/binary_search/concept) | remark | |
| brute-force-search-kmeans | ||
brute-force-search-kmeans (influential/kmeans_clustering/02_concept) | algorithm | |
| categorical-distribution | ||
categorical-distribution (influential/naive_bayes/02_concept) | definition | |
| categorical-distribution-example | ||
categorical-distribution-example (influential/naive_bayes/02_concept) | example | |
| categorical-distribution-gmm | ||
categorical-distribution-gmm (influential/gaussian_mixture_models/02_concept) | definition | |
| categorical-multinomial-distribution | ||
categorical-multinomial-distribution (influential/naive_bayes/02_concept) | definition | |
| categorical-multinomial-distribution-gmm | ||
categorical-multinomial-distribution-gmm (influential/gaussian_mixture_models/02_concept) | definition | |
| cicd-concept-pinning-pylint | ||
cicd-concept-pinning-pylint (operations/machine_learning_lifecycle/010_continuous_integration_deployment_learning_and_training) | example | |
| conditional-independence | ||
conditional-independence (influential/naive_bayes/02_concept) | definition | |
| cor:law-total-probability | ||
cor:law-total-probability (probability_theory/02_probability/0206_bayes_theorem) | corollary | |
| cor:moment_generating_function_sum_of_N_rv | ||
cor:moment_generating_function_sum_of_N_rv (probability_theory/06_sample_statistics/0601_moment_generating_and_characteristic_functions/moment_generating_function_application_sum_of_rv) | corollary | |
| cor_continuous_expectation | ||
cor_continuous_expectation (probability_theory/04_continuous_random_variables/0403_expectation) | corollary | |
| cor_iid_joint_pdf | ||
cor_iid_joint_pdf (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | corollary | |
| cor_probability_interval | ||
cor_probability_interval (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | corollary | |
| cor_standard_gaussian | ||
cor_standard_gaussian (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | corollary | |
| corollary:chebyshev-iid | ||
corollary:chebyshev-iid (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | corollary | |
| corollary:inclusion-exclusion | ||
corollary:inclusion-exclusion (probability_theory/02_probability/0203_probability_axioms) | corollary | |
| corollary:inequality-bounds | ||
corollary:inequality-bounds (probability_theory/02_probability/0203_probability_axioms) | corollary | |
| corollary:law_of_iterated_expectation | ||
corollary:law_of_iterated_expectation (probability_theory/05_joint_distributions/0504_conditional_expectation_variance/concept) | corollary | |
| corollary:positive_definite_matrix | ||
corollary:positive_definite_matrix (probability_theory/05_joint_distributions/0507_multivariate_gaussian/psd) | corollary | |
| corollary:probability-of-complements | ||
corollary:probability-of-complements (probability_theory/02_probability/0203_probability_axioms) | corollary | |
| corollary:probability-of-empty-set | ||
corollary:probability-of-empty-set (probability_theory/02_probability/0203_probability_axioms) | corollary | |
| cosine-similarity-definition | ||
cosine-similarity-definition (influential/vector_semantics_and_embeddings/cosine_similarity/concept) | definition | |
| criterion:kmeans-optimal-assignment | ||
criterion:kmeans-optimal-assignment (influential/kmeans_clustering/02_concept) | criterion | |
| criterion:kmeans-optimal-cluster-centers | ||
criterion:kmeans-optimal-cluster-centers (influential/kmeans_clustering/02_concept) | criterion | |
| dataset-definition | ||
dataset-definition (influential/naive_bayes/02_concept) | definition | |
| decoder-concept-attention-exact-match-scenario | ||
decoder-concept-attention-exact-match-scenario (influential/generative_pretrained_transformer/04_implementation) | example | |
| decoder-concept-attention-scores | ||
decoder-concept-attention-scores (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-concept-attention-scoring-function | ||
decoder-concept-attention-scoring-function (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-concept-attention-scoring-function-with-scaling | ||
decoder-concept-attention-scoring-function-with-scaling (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-concept-attention-scoring-function-with-scaling-softmax | ||
decoder-concept-attention-scoring-function-with-scaling-softmax (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-concept-context-vector-matrix | ||
decoder-concept-context-vector-matrix (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-concept-gradient-saturation | ||
decoder-concept-gradient-saturation (influential/generative_pretrained_transformer/04_implementation) | remark | |
| decoder-concept-linear-projections-queries-keys-values | ||
decoder-concept-linear-projections-queries-keys-values (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-concept-linear-projections-queries-keys-values-remark | ||
decoder-concept-linear-projections-queries-keys-values-remark (influential/generative_pretrained_transformer/04_implementation) | remark | |
| decoder-concept-numerical-stability | ||
decoder-concept-numerical-stability (influential/generative_pretrained_transformer/04_implementation) | remark | |
| decoder-concept-query-key-iid | ||
decoder-concept-query-key-iid (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-concept-scaled-dot-product-attention | ||
decoder-concept-scaled-dot-product-attention (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-concept-softmax-normalization-attention-weights | ||
decoder-concept-softmax-normalization-attention-weights (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-concept-variance-dot-product | ||
decoder-concept-variance-dot-product (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-layer-normalization | ||
decoder-layer-normalization (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-positional-encoding | ||
decoder-positional-encoding (influential/generative_pretrained_transformer/04_implementation) | definition | |
| decoder-simplified-objective-function | ||
decoder-simplified-objective-function (influential/generative_pretrained_transformer/03_concept) | remark | |
| def-conditional-likelihood-function-linear-regression | ||
def-conditional-likelihood-function-linear-regression (influential/linear_regression/02_concept) | definition | |
| def-conditional-log-likelihood-function-linear-regression | ||
def-conditional-log-likelihood-function-linear-regression (influential/linear_regression/02_concept) | definition | |
| def-cove-process | ||
def-cove-process (influential/cove/cove) | definition | |
| def-empirical-risk | ||
def-empirical-risk (influential/empirical_risk_minimization/02_concept) | definition | |
| def-gelu | ||
def-gelu (influential/generative_pretrained_transformer/04_implementation) | definition | |
| def-gelu-notation | ||
def-gelu-notation (influential/generative_pretrained_transformer/02_notations) | definition | |
| def-generalization-gap | ||
def-generalization-gap (influential/learning_theory/02_concept) | definition | |
| def-hallucination | ||
def-hallucination (influential/cove/cove) | definition | |
| def-loss-function | ||
def-loss-function (influential/loss_functions/02_concept) | definition | |
| def-loss-function-rv | ||
def-loss-function-rv (influential/loss_functions/02_concept) | definition | |
| def-marginal-pmf-pdf | ||
def-marginal-pmf-pdf (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | definition | |
| def-positionwise-ffn | ||
def-positionwise-ffn (influential/generative_pretrained_transformer/04_implementation) | definition | |
| def-positionwise-ffn-notation | ||
def-positionwise-ffn-notation (influential/generative_pretrained_transformer/02_notations) | definition | |
| def-r-squared | ||
def-r-squared (influential/linear_regression/02_concept) | definition | |
| def-sample-average | ||
def-sample-average (probability_theory/06_sample_statistics/0603_law_of_large_numbers/concept) | definition | |
| def-true-risk | ||
def-true-risk (influential/empirical_risk_minimization/02_concept) | definition | |
| def-voronoi-region | ||
def-voronoi-region (influential/kmeans_clustering/02_concept) | definition | |
| def:assignment | ||
def:assignment (influential/kmeans_clustering/02_concept) | definition | |
| def:bayes-theorem | ||
def:bayes-theorem (probability_theory/02_probability/0206_bayes_theorem) | definition | |
| def:bernoulli_trials_1 | ||
def:bernoulli_trials_1 (probability_theory/03_discrete_random_variables/bernoulli/0308_bernoulli_distribution_concept) | definition | |
| def:bernoulli_trials_2 | ||
def:bernoulli_trials_2 (probability_theory/03_discrete_random_variables/binomial/0309_binomial_distribution_concept) | definition | |
| def:binomial_as_sum_of_bernoulli | ||
def:binomial_as_sum_of_bernoulli (probability_theory/03_discrete_random_variables/binomial/0309_binomial_distribution_concept) | definition | |
| def:centroids | ||
def:centroids (influential/kmeans_clustering/02_concept) | definition | |
| def:characteristic_polynomial | ||
def:characteristic_polynomial (probability_theory/05_joint_distributions/0507_multivariate_gaussian/eigendecomposition) | definition | |
| def:conditional-cdf-of-a-continuous-random-variable | ||
def:conditional-cdf-of-a-continuous-random-variable (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | definition | |
| def:conditional-cdf-of-a-discrete-random-variable | ||
def:conditional-cdf-of-a-discrete-random-variable (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | definition | |
| def:conditional-independence | ||
def:conditional-independence (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | definition | |
| def:conditional-likelihood-machine-learning | ||
def:conditional-likelihood-machine-learning (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | definition | |
| def:conditional-pdf-of-a-continuous-random-variable | ||
def:conditional-pdf-of-a-continuous-random-variable (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | definition | |
| def:conditional-pmf | ||
def:conditional-pmf (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | definition | |
| def:conditional-variance | ||
def:conditional-variance (probability_theory/05_joint_distributions/0504_conditional_expectation_variance/concept) | definition | |
| def:conditional_expectation | ||
def:conditional_expectation (probability_theory/05_joint_distributions/0504_conditional_expectation_variance/concept) | definition | |
| def:contour_lines | ||
def:contour_lines (probability_theory/01_mathematical_preliminaries/03_contours) | definition | |
| def:contour_map | ||
def:contour_map (probability_theory/01_mathematical_preliminaries/03_contours) | definition | |
| def:correlation_coefficient | ||
def:correlation_coefficient (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | definition | |
| def:cosine_dot_product | ||
def:cosine_dot_product (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | definition | |
| def:covariance | ||
def:covariance (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | definition | |
| def:covariance-matrix | ||
def:covariance-matrix (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def:covariance_matrix_2d | ||
def:covariance_matrix_2d (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | definition | |
| def:decision_boundary | ||
def:decision_boundary (influential/decision_boundary/02_concept) | definition | |
| def:diagonalizable_matrix | ||
def:diagonalizable_matrix (probability_theory/05_joint_distributions/0507_multivariate_gaussian/eigendecomposition) | definition | |
| def:dichotomy | ||
def:dichotomy (influential/learning_theory/02_concept) | definition | |
| def:disjoint | ||
def:disjoint (probability_theory/02_probability/0205_independence) | definition | |
| def:eigendecomposition | ||
def:eigendecomposition (probability_theory/05_joint_distributions/0507_multivariate_gaussian/eigendecomposition) | definition | |
| def:eigenvalue | ||
def:eigenvalue (probability_theory/05_joint_distributions/0507_multivariate_gaussian/eigendecomposition) | definition | |
| def:expectation-random-vector | ||
def:expectation-random-vector (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def:geo | ||
def:geo (probability_theory/03_discrete_random_variables/geometric/0310_geometric_distribution_concept) | definition | |
| def:independence | ||
def:independence (probability_theory/05_joint_distributions/0507_multivariate_gaussian/concept) | definition | |
| def:independence-conditional | ||
def:independence-conditional (probability_theory/02_probability/0205_independence) | definition | |
| def:independent-events | ||
def:independent-events (probability_theory/02_probability/0205_independence) | definition | |
| def:independent-random-vector | ||
def:independent-random-vector (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def:joint-cdf-random-vector | ||
def:joint-cdf-random-vector (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def:joint-expectation-independent-random-vector | ||
def:joint-expectation-independent-random-vector (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def:joint_expectation | ||
def:joint_expectation (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | definition | |
| def:kmeans-cost | ||
def:kmeans-cost (influential/kmeans_clustering/02_concept) | definition | |
| def:kmeans-loss | ||
def:kmeans-loss (influential/kmeans_clustering/02_concept) | definition | |
| def:kmeans-objective | ||
def:kmeans-objective (influential/kmeans_clustering/02_concept) | definition | |
| def:kmeans-voronoi-partition | ||
def:kmeans-voronoi-partition (influential/kmeans_clustering/02_concept) | definition | |
| def:likelihood | ||
def:likelihood (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | definition | |
| def:likelihood-iid | ||
def:likelihood-iid (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | definition | |
| def:likelihood-iid-higher-dim | ||
def:likelihood-iid-higher-dim (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | definition | |
| def:likelihood-iid-supervised-learning | ||
def:likelihood-iid-supervised-learning (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | definition | |
| def:limiting-perspective | ||
def:limiting-perspective (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | definition | |
| def:log-likelihood | ||
def:log-likelihood (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | definition | |
| def:marginal-pdf-random-vector | ||
def:marginal-pdf-random-vector (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def:matrix_representation_of_a_eigenvalue_and_eigenvector | ||
def:matrix_representation_of_a_eigenvalue_and_eigenvector (probability_theory/05_joint_distributions/0507_multivariate_gaussian/eigendecomposition) | definition | |
| def:maximum-likelihood-estimation | ||
def:maximum-likelihood-estimation (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | definition | |
| def:maximum-likelihood-estimation-for-bernoulli-distribution | ||
def:maximum-likelihood-estimation-for-bernoulli-distribution (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | definition | |
| def:moment_generating_function | ||
def:moment_generating_function (probability_theory/06_sample_statistics/0601_moment_generating_and_characteristic_functions/moment_generating_function) | definition | |
| def:multivariate_gaussian | ||
def:multivariate_gaussian (probability_theory/05_joint_distributions/0507_multivariate_gaussian/concept) | definition | |
| def:multivariate_gaussian_distribution_2d | ||
def:multivariate_gaussian_distribution_2d (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | definition | |
| def:naive-bayes-likelihood | ||
def:naive-bayes-likelihood (influential/naive_bayes/02_concept) | definition | |
| def:naive-bayes-log-likelihood | ||
def:naive-bayes-log-likelihood (influential/naive_bayes/02_concept) | definition | |
| def:naive-bayes-max-feature-params | ||
def:naive-bayes-max-feature-params (influential/naive_bayes/02_concept) | definition | |
| def:naive-bayes-max-priors | ||
def:naive-bayes-max-priors (influential/naive_bayes/02_concept) | definition | |
| def:pdf-independent-random-vector | ||
def:pdf-independent-random-vector (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def:pdf-random-vector | ||
def:pdf-random-vector (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def:poi | ||
def:poi (probability_theory/03_discrete_random_variables/poisson/0311_poisson_distribution_concept) | definition | |
| def:positive_definite | ||
def:positive_definite (probability_theory/05_joint_distributions/0507_multivariate_gaussian/psd) | definition | |
| def:positive_semi_definite | ||
def:positive_semi_definite (probability_theory/05_joint_distributions/0507_multivariate_gaussian/psd) | definition | |
| def:random-vector | ||
def:random-vector (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def:state_space_binomial | ||
def:state_space_binomial (probability_theory/03_discrete_random_variables/binomial/0309_binomial_distribution_concept) | definition | |
| def_bernoulli_distribution_cdf | ||
def_bernoulli_distribution_cdf (probability_theory/03_discrete_random_variables/bernoulli/0308_bernoulli_distribution_concept) | definition | |
| def_bernoulli_distribution_pmf | ||
def_bernoulli_distribution_pmf (probability_theory/03_discrete_random_variables/bernoulli/0308_bernoulli_distribution_concept) | definition | |
| def_binomial_distribution_cdf | ||
def_binomial_distribution_cdf (probability_theory/03_discrete_random_variables/binomial/0309_binomial_distribution_concept) | definition | |
| def_binomial_distribution_pmf | ||
def_binomial_distribution_pmf (probability_theory/03_discrete_random_variables/binomial/0309_binomial_distribution_concept) | definition | |
| def_cdf | ||
def_cdf (probability_theory/03_discrete_random_variables/0304_cumulative_distribution_function) | definition | |
| def_continuous_cdf | ||
def_continuous_cdf (probability_theory/04_continuous_random_variables/0405_cumulative_distribution_function) | definition | |
| def_continuous_cdf_continuity | ||
def_continuous_cdf_continuity (probability_theory/04_continuous_random_variables/0405_cumulative_distribution_function) | definition | |
| def_continuous_expectation | ||
def_continuous_expectation (probability_theory/04_continuous_random_variables/0403_expectation) | definition | |
| def_continuous_random_variable | ||
def_continuous_random_variable (probability_theory/04_continuous_random_variables/0401_continuous_random_variables) | definition | |
| def_continuous_uniform_distribution_cdf | ||
def_continuous_uniform_distribution_cdf (probability_theory/04_continuous_random_variables/0407_continuous_uniform_distribution) | definition | |
| def_continuous_uniform_distribution_pdf | ||
def_continuous_uniform_distribution_pdf (probability_theory/04_continuous_random_variables/0407_continuous_uniform_distribution) | definition | |
| def_countable_set | ||
def_countable_set (probability_theory/03_discrete_random_variables/0302_discrete_random_variables) | definition | |
| def_discrete_expectation | ||
def_discrete_expectation (probability_theory/03_discrete_random_variables/0305_expectation) | definition | |
| def_discrete_random_variables | ||
def_discrete_random_variables (probability_theory/03_discrete_random_variables/0302_discrete_random_variables) | definition | |
| def_discrete_uniform_cdf | ||
def_discrete_uniform_cdf (probability_theory/03_discrete_random_variables/uniform/0307_discrete_uniform_distribution_concept) | definition | |
| def_discrete_uniform_pmf | ||
def_discrete_uniform_pmf (probability_theory/03_discrete_random_variables/uniform/0307_discrete_uniform_distribution_concept) | definition | |
| def_error_function | ||
def_error_function (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | definition | |
| def_exponential_distribution_cdf | ||
def_exponential_distribution_cdf (probability_theory/04_continuous_random_variables/0408_exponential_distribution) | definition | |
| def_exponential_distribution_pdf | ||
def_exponential_distribution_pdf (probability_theory/04_continuous_random_variables/0408_exponential_distribution) | definition | |
| def_gaussian_distribution_cdf | ||
def_gaussian_distribution_cdf (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | definition | |
| def_gaussian_distribution_pdf | ||
def_gaussian_distribution_pdf (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | definition | |
| def_iid | ||
def_iid (probability_theory/03_discrete_random_variables/iid) | definition | |
| def_iid_N | ||
def_iid_N (probability_theory/05_joint_distributions/0506_random_vectors/concept) | definition | |
| def_iid_restated | ||
def_iid_restated (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | definition | |
| def_independent | ||
def_independent (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | definition | |
| def_independent_n | ||
def_independent_n (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | definition | |
| def_joint_cdf | ||
def_joint_cdf (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | definition | |
| def_joint_cdf_cont | ||
def_joint_cdf_cont (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | definition | |
| def_joint_pdf | ||
def_joint_pdf (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | definition | |
| def_joint_pmf | ||
def_joint_pmf (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | definition | |
| def_moments | ||
def_moments (probability_theory/03_discrete_random_variables/0306_moments_and_variance) | definition | |
| def_moments_continuous | ||
def_moments_continuous (probability_theory/04_continuous_random_variables/0404_moments_and_variance) | definition | |
| def_pmf | ||
def_pmf (probability_theory/03_discrete_random_variables/0303_probability_mass_function) | definition | |
| def_probability_density_function | ||
def_probability_density_function (probability_theory/04_continuous_random_variables/0402_probability_density_function) | definition | |
| def_probability_density_function_1d | ||
def_probability_density_function_1d (probability_theory/04_continuous_random_variables/0402_probability_density_function) | definition | |
| def_standard_deviation | ||
def_standard_deviation (probability_theory/03_discrete_random_variables/0306_moments_and_variance) | definition | |
| def_standard_gaussian_distribution | ||
def_standard_gaussian_distribution (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | definition | |
| def_standard_normal_distribution_cdf | ||
def_standard_normal_distribution_cdf (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | definition | |
| def_state_space | ||
def_state_space (probability_theory/03_discrete_random_variables/0303_probability_mass_function) | definition | |
| def_uncountable_set | ||
def_uncountable_set (probability_theory/04_continuous_random_variables/0401_continuous_random_variables) | definition | |
| def_variance | ||
def_variance (probability_theory/03_discrete_random_variables/0306_moments_and_variance) | definition | |
| def_variance_alt | ||
def_variance_alt (probability_theory/03_discrete_random_variables/0306_moments_and_variance) | definition | |
| def_variance_continuous | ||
def_variance_continuous (probability_theory/04_continuous_random_variables/0404_moments_and_variance) | definition | |
| def_variance_continuous_alt | ||
def_variance_continuous_alt (probability_theory/04_continuous_random_variables/0404_moments_and_variance) | definition | |
| def_zero_measure | ||
def_zero_measure (probability_theory/04_continuous_random_variables/0402_probability_density_function) | definition | |
| definition-0 | ||
definition-0 (probability_theory/02_probability/0204_conditional_probability) | definition | |
| definition-2 | ||
definition-2 (influential/gradient_descent/02_concept) | definition | |
| definition:convex | ||
definition:convex (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | definition | |
| dir-deriv-theorem | ||
dir-deriv-theorem (influential/gradient_descent/02_concept) | theorem | |
| directional_derivative_example | ||
directional_derivative_example (influential/gradient_descent/02_concept) | example | |
| ece595_def4.6 | ||
ece595_def4.6 (influential/learning_theory/02_concept) | definition | |
| elbow-method | ||
elbow-method (influential/kmeans_clustering/02_concept) | algorithm | |
| event | ||
event (probability_theory/02_probability/0202_probability_space) | definition | |
| event_space | ||
event_space (probability_theory/02_probability/0202_probability_space) | definition | |
| ex:gmm-update-mixture-weights | ||
ex:gmm-update-mixture-weights (influential/gaussian_mixture_models/02_concept) | example | |
| ex:log-likelihood-bernoulli | ||
ex:log-likelihood-bernoulli (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | example | |
| ex:moment_generating_function_1 | ||
ex:moment_generating_function_1 (probability_theory/06_sample_statistics/0601_moment_generating_and_characteristic_functions/moment_generating_function) | example | |
| ex:moment_generating_function_2 | ||
ex:moment_generating_function_2 (probability_theory/06_sample_statistics/0601_moment_generating_and_characteristic_functions/moment_generating_function) | example | |
| ex:moment_generating_function_bernoulli | ||
ex:moment_generating_function_bernoulli (probability_theory/06_sample_statistics/0601_moment_generating_and_characteristic_functions/moment_generating_function) | example | |
| ex:poi | ||
ex:poi (probability_theory/03_discrete_random_variables/poisson/0311_poisson_distribution_concept) | example | |
| ex:poi2 | ||
ex:poi2 (probability_theory/03_discrete_random_variables/poisson/0311_poisson_distribution_concept) | example | |
| ex:two-coins | ||
ex:two-coins (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | example | |
| ex_gaussian_iid | ||
ex_gaussian_iid (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | example | |
| ex_gaussian_iid_cont | ||
ex_gaussian_iid_cont (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | example | |
| ex_iid_1 | ||
ex_iid_1 (probability_theory/03_discrete_random_variables/iid) | example | |
| example-4 | ||
example-4 (influential/gradient_descent/02_concept) | example | |
| example-bayes-optimal-classifier | ||
example-bayes-optimal-classifier (influential/empirical_risk_minimization/02_concept) | example | |
| example-empirical-risk | ||
example-empirical-risk (influential/empirical_risk_minimization/02_concept) | example | |
| example-gmm-initialization | ||
example-gmm-initialization (influential/gaussian_mixture_models/02_concept) | example | |
| example-marginal-pdf-bivariate-normal | ||
example-marginal-pdf-bivariate-normal (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | example | |
| example-naive-bayes-feature-1-class-2 | ||
example-naive-bayes-feature-1-class-2 (influential/naive_bayes/02_concept) | example | |
| example-pixels | ||
example-pixels (influential/kmeans_clustering/04_image_segmentation) | example | |
| example:assignment | ||
example:assignment (influential/kmeans_clustering/02_concept) | example | |
| example:conditional-independence | ||
example:conditional-independence (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | example | |
| example_cdf | ||
example_cdf (probability_theory/03_discrete_random_variables/0304_cumulative_distribution_function) | example | |
| example_growth_function | ||
example_growth_function (influential/learning_theory/02_concept) | example | |
| example_pmf_coin_toss | ||
example_pmf_coin_toss (probability_theory/03_discrete_random_variables/0303_probability_mass_function) | example | |
| example_pmf_two_dice_rolls | ||
example_pmf_two_dice_rolls (probability_theory/03_discrete_random_variables/0303_probability_mass_function) | example | |
| example_random_variable_coin_toss | ||
example_random_variable_coin_toss (probability_theory/03_discrete_random_variables/0301_random_variables) | example | |
| example_random_variable_dice_roll | ||
example_random_variable_dice_roll (probability_theory/03_discrete_random_variables/0301_random_variables) | example | |
| example_state_space_coin_toss | ||
example_state_space_coin_toss (probability_theory/03_discrete_random_variables/0303_probability_mass_function) | example | |
| example_state_space_dice_roll | ||
example_state_space_dice_roll (probability_theory/03_discrete_random_variables/0303_probability_mass_function) | example | |
| example_variable_vs_random_variable | ||
example_variable_vs_random_variable (probability_theory/03_discrete_random_variables/0301_random_variables) | example | |
| experiment | ||
experiment (probability_theory/02_probability/0202_probability_space) | definition | |
| fundamental_theorem_of_calculus | ||
fundamental_theorem_of_calculus (probability_theory/01_mathematical_preliminaries/02_calculus) | theorem | |
| fundamental_theorem_of_calculus_corollary | ||
fundamental_theorem_of_calculus_corollary (probability_theory/01_mathematical_preliminaries/02_calculus) | corollary | |
| gd-algo | ||
gd-algo (influential/gradient_descent/02_concept) | algorithm | |
| gpt-notations-one-hot-example | ||
gpt-notations-one-hot-example (influential/generative_pretrained_transformer/04_implementation) | example | |
| gpt-notations-one-hot-example-dup | ||
gpt-notations-one-hot-example-dup (influential/generative_pretrained_transformer/02_notations) | example | |
| grad_vec | ||
grad_vec (influential/gradient_descent/02_concept) | definition | |
| how-does-softmax-work-additivity | ||
how-does-softmax-work-additivity (playbook/why_softmax_preserves_order_translation_invariant_not_invariant_scaling) | axiom | |
| how-does-softmax-work-non-negativity | ||
how-does-softmax-work-non-negativity (playbook/why_softmax_preserves_order_translation_invariant_not_invariant_scaling) | axiom | |
| how-does-softmax-work-normalization | ||
how-does-softmax-work-normalization (playbook/why_softmax_preserves_order_translation_invariant_not_invariant_scaling) | axiom | |
| iid-assumption | ||
iid-assumption (influential/naive_bayes/02_concept) | definition | |
| jacobian-softmax | ||
jacobian-softmax (playbook/why_softmax_preserves_order_translation_invariant_not_invariant_scaling) | definition | |
| joint-and-conditional-probability | ||
joint-and-conditional-probability (influential/naive_bayes/02_concept) | definition | |
| joint-distribution-example | ||
joint-distribution-example (influential/naive_bayes/02_concept) | example | |
| kmeans-monotonic-decrease | ||
kmeans-monotonic-decrease (influential/kmeans_clustering/02_concept) | lemma | |
| lagrangian-method | ||
lagrangian-method (influential/naive_bayes/02_concept) | definition | |
| lemma-hallucination-factors | ||
lemma-hallucination-factors (influential/cove/cove) | lemma | |
| lemma:hoeffding | ||
lemma:hoeffding (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | lemma | |
| likelihood | ||
likelihood (influential/naive_bayes/02_concept) | definition | |
| linear-algebra-01-preliminaries-field | ||
linear-algebra-01-preliminaries-field (linear_algebra/01_preliminaries/01-fields) | definition | |
| linear-algebra-02-vectors-04-vector-products-dot-product-example-1 | ||
linear-algebra-02-vectors-04-vector-products-dot-product-example-1 (linear_algebra/02_vectors/04-vector-products) | example | |
| linear-algebra-preliminaries-fields-on-the-real-numbers | ||
linear-algebra-preliminaries-fields-on-the-real-numbers (linear_algebra/01_preliminaries/01-fields) | example | |
| linear-search-loop-invariant-theorem | ||
linear-search-loop-invariant-theorem (dsa/searching_algorithms/linear_search/concept) | theorem | |
| lloyd-kmeans-algorithm | ||
lloyd-kmeans-algorithm (influential/kmeans_clustering/02_concept) | algorithm | |
| marginal-distribution-and-normalization-constant | ||
marginal-distribution-and-normalization-constant (influential/naive_bayes/02_concept) | definition | |
| master-theorem-generic-divide-and-conquer-algorithm | ||
master-theorem-generic-divide-and-conquer-algorithm (dsa/complexity_analysis/master_theorem) | algorithm | |
| matrix-formulation-softmax | ||
matrix-formulation-softmax (playbook/why_softmax_preserves_order_translation_invariant_not_invariant_scaling) | definition | |
| measure_zero_sets | ||
measure_zero_sets (probability_theory/02_probability/0202_probability_space) | definition | |
| ml-lifecycle-02-ranking-items-newsfeed | ||
ml-lifecycle-02-ranking-items-newsfeed (operations/machine_learning_lifecycle/02_project_scoping) | example | |
| ml-lifecycle-032-normalization | ||
ml-lifecycle-032-normalization (operations/machine_learning_lifecycle/03_dataops_pipeline/032_data_model_and_storage) | example | |
| monotone-convergence | ||
monotone-convergence (influential/kmeans_clustering/02_concept) | lemma | |
| naive-bayes-inference-algorithm | ||
naive-bayes-inference-algorithm (influential/naive_bayes/02_concept) | algorithm | |
| notation-overload | ||
notation-overload (influential/naive_bayes/02_concept) | remark | |
| obs-complexity | ||
obs-complexity (influential/cove/cove) | observation | |
| omniverse-dsa-searching-algorithms-binary-search-recursive-algorithm-correctness | ||
omniverse-dsa-searching-algorithms-binary-search-recursive-algorithm-correctness (dsa/searching_algorithms/binary_search/concept) | theorem | |
| parameter-vector | ||
parameter-vector (influential/naive_bayes/02_concept) | definition | |
| posterior | ||
posterior (influential/naive_bayes/02_concept) | definition | |
| pre_image | ||
pre_image (probability_theory/03_discrete_random_variables/0301_random_variables) | definition | |
| prf-example-conditional-expectation | ||
prf-example-conditional-expectation (influential/linear_regression/02_concept) | example | |
| prf-example-learner | ||
prf-example-learner (influential/linear_regression/02_concept) | example | |
| prf-gmm-update-covariance-example | ||
prf-gmm-update-covariance-example (influential/gaussian_mixture_models/02_concept) | example | |
| prf-gmm-update-means-example | ||
prf-gmm-update-means-example (influential/gaussian_mixture_models/02_concept) | example | |
| prf-remark-iid | ||
prf-remark-iid (influential/linear_regression/02_concept) | remark | |
| prf-remark-notation-convention-linear-regression | ||
prf-remark-notation-convention-linear-regression (influential/linear_regression/02_concept) | remark | |
| prf-remark-x-random | ||
prf-remark-x-random (influential/linear_regression/02_concept) | remark | |
| prf:algorithm-label-binarize | ||
prf:algorithm-label-binarize (influential/evaluation_metrics/classification/precision_recall_f1) | algorithm | |
| prf:definition | ||
prf:definition (influential/evaluation_metrics/classification/precision_recall_f1) | definition | |
| prf:definition-f1 | ||
prf:definition-f1 (influential/evaluation_metrics/classification/precision_recall_f1) | definition | |
| prf:definition-fnr | ||
prf:definition-fnr (influential/evaluation_metrics/classification/precision_recall_f1) | definition | |
| prf:definition-fpr | ||
prf:definition-fpr (influential/evaluation_metrics/classification/precision_recall_f1) | definition | |
| prf:definition-recall | ||
prf:definition-recall (influential/evaluation_metrics/classification/precision_recall_f1) | definition | |
| prf:definition-specificity | ||
prf:definition-specificity (influential/evaluation_metrics/classification/precision_recall_f1) | definition | |
| prf:definition:in-sample-error | ||
prf:definition:in-sample-error (influential/learning_theory/02_concept) | definition | |
| prf:definition:out-sample-error | ||
prf:definition:out-sample-error (influential/learning_theory/02_concept) | definition | |
| prf:definition:zero-one-loss | ||
prf:definition:zero-one-loss (influential/learning_theory/02_concept) | definition | |
| prf:example-bernoulli-parameter | ||
prf:example-bernoulli-parameter (probability_theory/08_estimation_theory/intro) | example | |
| prf:example-bits | ||
prf:example-bits (influential/kmeans_clustering/04_image_segmentation) | example | |
| prf:example-f1 | ||
prf:example-f1 (influential/evaluation_metrics/classification/precision_recall_f1) | example | |
| prf:example-gaussian-parameter | ||
prf:example-gaussian-parameter (probability_theory/08_estimation_theory/intro) | example | |
| prf:example-gmm-1 | ||
prf:example-gmm-1 (influential/gaussian_mixture_models/02_concept) | example | |
| prf:example-multiclass-benign | ||
prf:example-multiclass-benign (influential/evaluation_metrics/classification/precision_recall_f1) | example | |
| prf:example-multiclass-borderline | ||
prf:example-multiclass-borderline (influential/evaluation_metrics/classification/precision_recall_f1) | example | |
| prf:example-multiclass-malignant | ||
prf:example-multiclass-malignant (influential/evaluation_metrics/classification/precision_recall_f1) | example | |
| prf:example-precision | ||
prf:example-precision (influential/evaluation_metrics/classification/precision_recall_f1) | example | |
| prf:example-recall | ||
prf:example-recall (influential/evaluation_metrics/classification/precision_recall_f1) | example | |
| prf:naive-bayes-estimation-algorithm | ||
prf:naive-bayes-estimation-algorithm (influential/naive_bayes/02_concept) | algorithm | |
| prf:remark-bias | ||
prf:remark-bias (influential/linear_regression/02_concept) | remark | |
| prf:remark-bounding-the-entire-hypothesis-set | ||
prf:remark-bounding-the-entire-hypothesis-set (influential/learning_theory/02_concept) | remark | |
| prf:remark-gmm-closed-form | ||
prf:remark-gmm-closed-form (influential/gaussian_mixture_models/02_concept) | remark | |
| prf:remark-major-confusion-alert | ||
prf:remark-major-confusion-alert (influential/learning_theory/02_concept) | remark | |
| prf:remark-notation-gmm | ||
prf:remark-notation-gmm (influential/gaussian_mixture_models/02_concept) | remark | |
| prf:remark:kmeans-optimal-cluster-centers-notation | ||
prf:remark:kmeans-optimal-cluster-centers-notation (influential/kmeans_clustering/02_concept) | remark | |
| prf:remark:why_contours_of_multivariate_gaussian_are_elliptical | ||
prf:remark:why_contours_of_multivariate_gaussian_are_elliptical (probability_theory/05_joint_distributions/0507_multivariate_gaussian/geometry_of_multivariate_gaussian) | remark | |
| prior | ||
prior (influential/naive_bayes/02_concept) | definition | |
| probability-theory-central-moments | ||
probability-theory-central-moments (probability_theory/04_continuous_random_variables/0410_skewness_and_kurtosis) | definition | |
| probability-theory-mean-from-cdf | ||
probability-theory-mean-from-cdf (probability_theory/04_continuous_random_variables/0406_mean_median_mode) | theorem | |
| probability-theory-mean-from-cdf-x-gt-0 | ||
probability-theory-mean-from-cdf-x-gt-0 (probability_theory/04_continuous_random_variables/0406_mean_median_mode) | lemma | |
| probability-theory-mean-from-cdf-x-lt-0 | ||
probability-theory-mean-from-cdf-x-lt-0 (probability_theory/04_continuous_random_variables/0406_mean_median_mode) | lemma | |
| probability-theory-median | ||
probability-theory-median (probability_theory/04_continuous_random_variables/0406_mean_median_mode) | definition | |
| probability-theory-median-from-cdf | ||
probability-theory-median-from-cdf (probability_theory/04_continuous_random_variables/0406_mean_median_mode) | theorem | |
| probability-theory-mode | ||
probability-theory-mode (probability_theory/04_continuous_random_variables/0406_mean_median_mode) | definition | |
| probability_law | ||
probability_law (probability_theory/02_probability/0202_probability_space) | definition | |
| prop:bernoulli | ||
prop:bernoulli (probability_theory/03_discrete_random_variables/bernoulli/0308_bernoulli_distribution_concept) | property | |
| prop:bernoulli_var | ||
prop:bernoulli_var (probability_theory/03_discrete_random_variables/bernoulli/0308_bernoulli_distribution_concept) | property | |
| prop:bino_exp | ||
prop:bino_exp (probability_theory/03_discrete_random_variables/binomial/0309_binomial_distribution_concept) | property | |
| prop:bino_var | ||
prop:bino_var (probability_theory/03_discrete_random_variables/binomial/0309_binomial_distribution_concept) | property | |
| prop:conditional-probability-equalities | ||
prop:conditional-probability-equalities (probability_theory/02_probability/0204_conditional_probability) | proposition | |
| prop:correlation_coefficient | ||
prop:correlation_coefficient (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | property | |
| prop:covariance | ||
prop:covariance (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | property | |
| prop:geo_exp | ||
prop:geo_exp (probability_theory/03_discrete_random_variables/geometric/0310_geometric_distribution_concept) | property | |
| prop:geo_var | ||
prop:geo_var (probability_theory/03_discrete_random_variables/geometric/0310_geometric_distribution_concept) | property | |
| prop:mean_vector_covariance_matrix | ||
prop:mean_vector_covariance_matrix (probability_theory/05_joint_distributions/0507_multivariate_gaussian/concept) | property | |
| prop:poi_exp | ||
prop:poi_exp (probability_theory/03_discrete_random_variables/poisson/0311_poisson_distribution_concept) | property | |
| prop:poi_var | ||
prop:poi_var (probability_theory/03_discrete_random_variables/poisson/0311_poisson_distribution_concept) | property | |
| prop_continuous_cdf_interval | ||
prop_continuous_cdf_interval (probability_theory/04_continuous_random_variables/0405_cumulative_distribution_function) | proposition | |
| prop_continuous_discrete_cdf | ||
prop_continuous_discrete_cdf (probability_theory/04_continuous_random_variables/0405_cumulative_distribution_function) | proposition | |
| prop_dc_shift | ||
prop_dc_shift (probability_theory/03_discrete_random_variables/0306_moments_and_variance) | property | |
| prop_expectation_dc_shift_continuous | ||
prop_expectation_dc_shift_continuous (probability_theory/04_continuous_random_variables/0403_expectation) | property | |
| prop_expectation_dc_shift_discrete | ||
prop_expectation_dc_shift_discrete (probability_theory/03_discrete_random_variables/0305_expectation) | property | |
| prop_expectation_function_continuous | ||
prop_expectation_function_continuous (probability_theory/04_continuous_random_variables/0403_expectation) | property | |
| prop_expectation_function_discrete | ||
prop_expectation_function_discrete (probability_theory/03_discrete_random_variables/0305_expectation) | property | |
| prop_expectation_linearity_continuous | ||
prop_expectation_linearity_continuous (probability_theory/04_continuous_random_variables/0403_expectation) | property | |
| prop_expectation_linearity_discrete | ||
prop_expectation_linearity_discrete (probability_theory/03_discrete_random_variables/0305_expectation) | property | |
| prop_expectation_scaling_continuous | ||
prop_expectation_scaling_continuous (probability_theory/04_continuous_random_variables/0403_expectation) | property | |
| prop_expectation_scaling_discrete | ||
prop_expectation_scaling_discrete (probability_theory/03_discrete_random_variables/0305_expectation) | property | |
| prop_expectation_stronger_linearity_continuous | ||
prop_expectation_stronger_linearity_continuous (probability_theory/04_continuous_random_variables/0403_expectation) | property | |
| prop_expectation_stronger_linearity_discrete | ||
prop_expectation_stronger_linearity_discrete (probability_theory/03_discrete_random_variables/0305_expectation) | property | |
| prop_linearity | ||
prop_linearity (probability_theory/03_discrete_random_variables/0306_moments_and_variance) | property | |
| prop_scaling | ||
prop_scaling (probability_theory/03_discrete_random_variables/0306_moments_and_variance) | property | |
| prop_sum_poi | ||
prop_sum_poi (probability_theory/03_discrete_random_variables/poisson/0311_poisson_distribution_concept) | property | |
| random_variables | ||
random_variables (probability_theory/03_discrete_random_variables/0301_random_variables) | definition | |
| rem-erm-trial-and-error | ||
rem-erm-trial-and-error (influential/empirical_risk_minimization/02_concept) | remark | |
| rem-iid-erm | ||
rem-iid-erm (influential/empirical_risk_minimization/02_concept) | remark | |
| rem-risk-vs-loss | ||
rem-risk-vs-loss (influential/empirical_risk_minimization/02_concept) | remark | |
| rem:gmm-update-mixture-weights-depends-on-all-parameters | ||
rem:gmm-update-mixture-weights-depends-on-all-parameters (influential/gaussian_mixture_models/02_concept) | remark | |
| rem:likelihood | ||
rem:likelihood (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | remark | |
| rem:where-y | ||
rem:where-y (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | remark | |
| rem_exponential_distribution_pdf | ||
rem_exponential_distribution_pdf (probability_theory/04_continuous_random_variables/0408_exponential_distribution) | remark | |
| rem_iid | ||
rem_iid (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | remark | |
| rem_open_equals_closed_interval | ||
rem_open_equals_closed_interval (probability_theory/04_continuous_random_variables/0402_probability_density_function) | remark | |
| rem_probability_density_function | ||
rem_probability_density_function (probability_theory/04_continuous_random_variables/0402_probability_density_function) | remark | |
| remark-0 | ||
remark-0 (dsa/hash_map/questions/01-two-sum) | remark | |
| remark-4 | ||
remark-4 (influential/cove/cove) | remark | |
| remark-6 | ||
remark-6 (influential/cove/cove) | remark | |
| remark-approx-gelu | ||
remark-approx-gelu (influential/generative_pretrained_transformer/04_implementation) | remark | |
| remark-approx-gelu-notation | ||
remark-approx-gelu-notation (influential/generative_pretrained_transformer/02_notations) | remark | |
| remark-bayes-optimal-classifier | ||
remark-bayes-optimal-classifier (influential/empirical_risk_minimization/03_bayes_optimal_classifier) | remark | |
| remark-bayes-optimal-classifier-naive-bayes | ||
remark-bayes-optimal-classifier-naive-bayes (influential/empirical_risk_minimization/03_bayes_optimal_classifier) | remark | |
| remark-empirical-parameters | ||
remark-empirical-parameters (influential/naive_bayes/02_concept) | remark | |
| remark-finding-cdf-is-easier | ||
remark-finding-cdf-is-easier (probability_theory/04_continuous_random_variables/0412_functions_of_random_variables) | remark | |
| remark-gmm-update-means | ||
remark-gmm-update-means (influential/gaussian_mixture_models/02_concept) | remark | |
| remark-interpretation-true-risk | ||
remark-interpretation-true-risk (influential/empirical_risk_minimization/02_concept) | remark | |
| remark-joint-pdf | ||
remark-joint-pdf (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | remark | |
| remark-joint-pmf | ||
remark-joint-pmf (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | remark | |
| remark-kmeans-greedy | ||
remark-kmeans-greedy (influential/kmeans_clustering/02_concept) | remark | |
| remark-kmeans-problem-statement | ||
remark-kmeans-problem-statement (influential/kmeans_clustering/02_concept) | remark | |
| remark-learning-problem-notations | ||
remark-learning-problem-notations (influential/learning_theory/02_concept) | remark | |
| remark-learning-problem-notations-learning-theory | ||
remark-learning-problem-notations-learning-theory (influential/learning_theory/02_concept) | remark | |
| remark-likelihood-function-notation-clash | ||
remark-likelihood-function-notation-clash (influential/linear_regression/02_concept) | remark | |
| remark-marginal-distribution-ltp | ||
remark-marginal-distribution-ltp (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | remark | |
| remark-notation | ||
remark-notation (influential/cove/cove) | remark | |
| remark-random-variable-is-a-function | ||
remark-random-variable-is-a-function (influential/learning_theory/02_concept) | remark | |
| remark-summary-1 | ||
remark-summary-1 (influential/learning_theory/02_concept) | remark | |
| remark-things-to-note | ||
remark-things-to-note (influential/learning_theory/02_concept) | remark | |
| remark-univariate-mle | ||
remark-univariate-mle (influential/naive_bayes/02_concept) | remark | |
| remark-what-is-a-joint-distribution | ||
remark-what-is-a-joint-distribution (probability_theory/05_joint_distributions/from_single_variable_to_joint_distributions) | remark | |
| remark:cauchy_schwarz | ||
remark:cauchy_schwarz (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | remark | |
| remark:conditional-distribution-is-a-distribution-for-a-sub-population | ||
remark:conditional-distribution-is-a-distribution-for-a-sub-population (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | remark | |
| remark:conditional-expectation-is-the-expectation-for-a-sub-population | ||
remark:conditional-expectation-is-the-expectation-for-a-sub-population (probability_theory/05_joint_distributions/0504_conditional_expectation_variance/concept) | remark | |
| remark:conditional-pmf | ||
remark:conditional-pmf (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | remark | |
| remark:convex_concave | ||
remark:convex_concave (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | remark | |
| remark:cost-function-is-a-function-of-assignment-and-centroids | ||
remark:cost-function-is-a-function-of-assignment-and-centroids (influential/kmeans_clustering/02_concept) | remark | |
| remark:iid_assumption | ||
remark:iid_assumption (probability_theory/05_joint_distributions/0507_multivariate_gaussian/concept) | remark | |
| remark:kmeans-cost-function-is-a-function-of-assignments-and-cluster-centers | ||
remark:kmeans-cost-function-is-a-function-of-assignments-and-cluster-centers (influential/kmeans_clustering/02_concept) | remark | |
| remark:union_bound_tightness | ||
remark:union_bound_tightness (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | remark | |
| remove-duplicates-from-sorted-array-two-pointers-algorithm-1 | ||
remove-duplicates-from-sorted-array-two-pointers-algorithm-1 (dsa/two_pointers/questions/two_pointers/26-remove-duplicates-from-sorted-array) | algorithm | |
| remove-duplicates-from-sorted-array-two-pointers-algorithm-2 | ||
remove-duplicates-from-sorted-array-two-pointers-algorithm-2 (dsa/two_pointers/questions/two_pointers/26-remove-duplicates-from-sorted-array) | algorithm | |
| remove-duplicates-from-sorted-array-two-pointers-claim | ||
remove-duplicates-from-sorted-array-two-pointers-claim (dsa/two_pointers/questions/two_pointers/26-remove-duplicates-from-sorted-array) | theorem | |
| restricted_hypothesis_space | ||
restricted_hypothesis_space (influential/learning_theory/02_concept) | definition | |
| rmk:infinite-hypothesis-space | ||
rmk:infinite-hypothesis-space (influential/learning_theory/02_concept) | remark | |
| rmk:maximum-likelihood-estimation | ||
rmk:maximum-likelihood-estimation (probability_theory/08_estimation_theory/maximum_likelihood_estimation/concept) | remark | |
| rmk:random-vector | ||
rmk:random-vector (probability_theory/05_joint_distributions/0506_random_vectors/concept) | remark | |
| rmk_continuous_uniform_distribution | ||
rmk_continuous_uniform_distribution (probability_theory/04_continuous_random_variables/0407_continuous_uniform_distribution) | remark | |
| rmk_gaussian_distribution_pdf | ||
rmk_gaussian_distribution_pdf (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | remark | |
| sample_complexity_example | ||
sample_complexity_example (influential/learning_theory/02_concept) | example | |
| sample_space | ||
sample_space (probability_theory/02_probability/0202_probability_space) | definition | |
| sauer's_lemma | ||
sauer's_lemma (influential/learning_theory/02_concept) | lemma | |
| shatters | ||
shatters (influential/learning_theory/02_concept) | definition | |
| softmax-output-vector | ||
softmax-output-vector (playbook/why_softmax_preserves_order_translation_invariant_not_invariant_scaling) | definition | |
| software-engineering-concurrency-parallelism-asynchronous-generator-yield-is-an-expression | ||
software-engineering-concurrency-parallelism-asynchronous-generator-yield-is-an-expression (software_engineering/concurrency_parallelism_asynchronous/generator_yield) | remark | |
| software-engineering-concurrency-parallelism-asynchronous-generator-yield-remark | ||
software-engineering-concurrency-parallelism-asynchronous-generator-yield-remark (software_engineering/concurrency_parallelism_asynchronous/generator_yield) | remark | |
| some-remarks | ||
some-remarks (influential/naive_bayes/02_concept) | remark | |
| stack-list-amortized-worst-case-time-complexity | ||
stack-list-amortized-worst-case-time-complexity (dsa/stack/concept) | remark | |
| stack-list-remarks | ||
stack-list-remarks (dsa/stack/concept) | remark | |
| stirling-numbers | ||
stirling-numbers (influential/kmeans_clustering/02_concept) | lemma | |
| term-document-example-info-retrieval | ||
term-document-example-info-retrieval (influential/vector_semantics_and_embeddings/words_and_vectors/concept) | example | |
| term-document-remark | ||
term-document-remark (influential/vector_semantics_and_embeddings/words_and_vectors/concept) | remark | |
| theorem-3 | ||
theorem-3 (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | theorem | |
| theorem-empirical-risk-minimization | ||
theorem-empirical-risk-minimization (influential/empirical_risk_minimization/02_concept) | theorem | |
| theorem-erm-approximates-trm | ||
theorem-erm-approximates-trm (influential/empirical_risk_minimization/02_concept) | theorem | |
| theorem-expectation-of-sample-average | ||
theorem-expectation-of-sample-average (probability_theory/06_sample_statistics/0603_law_of_large_numbers/concept) | theorem | |
| theorem-gmm-update-covariance | ||
theorem-gmm-update-covariance (influential/gaussian_mixture_models/02_concept) | theorem | |
| theorem-gmm-update-means | ||
theorem-gmm-update-means (influential/gaussian_mixture_models/02_concept) | theorem | |
| theorem-hoeffding-inequality-restated | ||
theorem-hoeffding-inequality-restated (influential/learning_theory/02_concept) | theorem | |
| theorem-learning-theory-1 | ||
theorem-learning-theory-1 (influential/learning_theory/02_concept) | theorem | |
| theorem-strong-law-of-large-numbers | ||
theorem-strong-law-of-large-numbers (probability_theory/06_sample_statistics/0603_law_of_large_numbers/concept) | theorem | |
| theorem-true-risk-minimization | ||
theorem-true-risk-minimization (influential/empirical_risk_minimization/02_concept) | theorem | |
| theorem-variance-of-sample-average | ||
theorem-variance-of-sample-average (probability_theory/06_sample_statistics/0603_law_of_large_numbers/concept) | theorem | |
| theorem-weak-law-of-large-numbers | ||
theorem-weak-law-of-large-numbers (probability_theory/06_sample_statistics/0603_law_of_large_numbers/concept) | theorem | |
| theorem-weak-law-of-large-numbers-restated | ||
theorem-weak-law-of-large-numbers-restated (influential/learning_theory/02_concept) | theorem | |
| theorem:cauchy_schwarz | ||
theorem:cauchy_schwarz (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | theorem | |
| theorem:chebyshev | ||
theorem:chebyshev (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | theorem | |
| theorem:chernoff-bound | ||
theorem:chernoff-bound (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | theorem | |
| theorem:convolutions-of-random-variables | ||
theorem:convolutions-of-random-variables (probability_theory/05_joint_distributions/0505_sum_of_random_variables/concept) | theorem | |
| theorem:hoeffding | ||
theorem:hoeffding (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | theorem | |
| theorem:jensen | ||
theorem:jensen (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | theorem | |
| theorem:law_of_total_expectation | ||
theorem:law_of_total_expectation (probability_theory/05_joint_distributions/0504_conditional_expectation_variance/concept) | theorem | |
| theorem:markov | ||
theorem:markov (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | theorem | |
| theorem:method-of-transformations | ||
theorem:method-of-transformations (probability_theory/04_continuous_random_variables/0412_functions_of_random_variables) | theorem | |
| theorem:positive_semi_definite_covariance_matrix | ||
theorem:positive_semi_definite_covariance_matrix (probability_theory/05_joint_distributions/0507_multivariate_gaussian/psd) | theorem | |
| theorem:positive_semi_definite_matrix | ||
theorem:positive_semi_definite_matrix (probability_theory/05_joint_distributions/0507_multivariate_gaussian/psd) | theorem | |
| theorem:sum-of-common-distributions | ||
theorem:sum-of-common-distributions (probability_theory/05_joint_distributions/0505_sum_of_random_variables/concept) | theorem | |
| theorem:sum-of-gaussian-random-variables | ||
theorem:sum-of-gaussian-random-variables (probability_theory/05_joint_distributions/0505_sum_of_random_variables/concept) | theorem | |
| theorem:sum-of-poisson-random-variables | ||
theorem:sum-of-poisson-random-variables (probability_theory/05_joint_distributions/0505_sum_of_random_variables/concept) | theorem | |
| theorem:union_bound | ||
theorem:union_bound (probability_theory/06_sample_statistics/0602_probability_inequalities/concept) | theorem | |
| thm:cauchy_schwarz_inequality | ||
thm:cauchy_schwarz_inequality (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | theorem | |
| thm:conditional-pdf-of-an-event-given-y | ||
thm:conditional-pdf-of-an-event-given-y (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | theorem | |
| thm:conditional-pmf-of-an-event-a-given-y | ||
thm:conditional-pmf-of-an-event-a-given-y (probability_theory/05_joint_distributions/0503_conditional_pmf_pdf/concept) | theorem | |
| thm:covariance | ||
thm:covariance (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | theorem | |
| thm:covariance-matrix-independent | ||
thm:covariance-matrix-independent (probability_theory/05_joint_distributions/0506_random_vectors/concept) | theorem | |
| thm:disjoint-vs-independent | ||
thm:disjoint-vs-independent (probability_theory/02_probability/0205_independence) | theorem | |
| thm:eigenvalues_are_roots_of_the_characteristic_polynomial | ||
thm:eigenvalues_are_roots_of_the_characteristic_polynomial (probability_theory/05_joint_distributions/0507_multivariate_gaussian/eigendecomposition) | theorem | |
| thm:eigenvalues_of_a_symmetric_matrix | ||
thm:eigenvalues_of_a_symmetric_matrix (probability_theory/05_joint_distributions/0507_multivariate_gaussian/eigendecomposition) | theorem | |
| thm:empirical_correlation_coefficient | ||
thm:empirical_correlation_coefficient (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | theorem | |
| thm:equivalent_conditions_for_lambda_to_be_an_eigenvalue | ||
thm:equivalent_conditions_for_lambda_to_be_an_eigenvalue (probability_theory/05_joint_distributions/0507_multivariate_gaussian/eigendecomposition) | theorem | |
| thm:generalization-bound | ||
thm:generalization-bound (influential/learning_theory/02_concept) | theorem | |
| thm:gmm-update-mixture-weights | ||
thm:gmm-update-mixture-weights (influential/gaussian_mixture_models/02_concept) | theorem | |
| thm:independence_and_covariance | ||
thm:independence_and_covariance (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | theorem | |
| thm:independence_and_joint_expectation | ||
thm:independence_and_joint_expectation (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | theorem | |
| thm:law-total-probability | ||
thm:law-total-probability (probability_theory/02_probability/0206_bayes_theorem) | theorem | |
| thm:linear_transformation_mean_covariance | ||
thm:linear_transformation_mean_covariance (probability_theory/05_joint_distributions/0507_multivariate_gaussian/application_transformation) | theorem | |
| thm:linearity_of_covariance | ||
thm:linearity_of_covariance (probability_theory/05_joint_distributions/0502_joint_expectation_and_correlation/concept) | theorem | |
| thm:minimizing-individual-clusters-cost-is-equivalent-to-minimizing-the-objective-function | ||
thm:minimizing-individual-clusters-cost-is-equivalent-to-minimizing-the-objective-function (influential/kmeans_clustering/02_concept) | theorem | |
| thm:moment_generating_function_properties | ||
thm:moment_generating_function_properties (probability_theory/06_sample_statistics/0601_moment_generating_and_characteristic_functions/moment_generating_function) | theorem | |
| thm:moment_generating_function_sum_of_2_rv | ||
thm:moment_generating_function_sum_of_2_rv (probability_theory/06_sample_statistics/0601_moment_generating_and_characteristic_functions/moment_generating_function_application_sum_of_rv) | theorem | |
| thm:moment_generating_function_sum_of_gaussian_rv | ||
thm:moment_generating_function_sum_of_gaussian_rv (probability_theory/06_sample_statistics/0601_moment_generating_and_characteristic_functions/moment_generating_function_application_sum_of_rv) | theorem | |
| thm:moment_generating_function_sum_of_poisson_rv | ||
thm:moment_generating_function_sum_of_poisson_rv (probability_theory/06_sample_statistics/0601_moment_generating_and_characteristic_functions/moment_generating_function_application_sum_of_rv) | theorem | |
| thm:orthornormal_basis | ||
thm:orthornormal_basis (probability_theory/05_joint_distributions/0507_multivariate_gaussian/eigendecomposition) | theorem | |
| thm:poi_bin | ||
thm:poi_bin (probability_theory/03_discrete_random_variables/poisson/0311_poisson_distribution_concept) | theorem | |
| thm:shifting_mean_covariance | ||
thm:shifting_mean_covariance (probability_theory/05_joint_distributions/0507_multivariate_gaussian/application_transformation) | theorem | |
| thm_cdf | ||
thm_cdf (probability_theory/03_discrete_random_variables/0304_cumulative_distribution_function) | theorem | |
| thm_cdf_arbitrary_gaussian_distribution | ||
thm_cdf_arbitrary_gaussian_distribution (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | theorem | |
| thm_cdf_point | ||
thm_cdf_point (probability_theory/04_continuous_random_variables/0405_cumulative_distribution_function) | theorem | |
| thm_cdf_right_continuous | ||
thm_cdf_right_continuous (probability_theory/04_continuous_random_variables/0405_cumulative_distribution_function) | theorem | |
| thm_continuous_uniform_distribution | ||
thm_continuous_uniform_distribution (probability_theory/04_continuous_random_variables/0407_continuous_uniform_distribution) | theorem | |
| thm_existence_of_expectation_continuous | ||
thm_existence_of_expectation_continuous (probability_theory/04_continuous_random_variables/0403_expectation) | theorem | |
| thm_existence_of_expectation_discrete | ||
thm_existence_of_expectation_discrete (probability_theory/03_discrete_random_variables/0305_expectation) | theorem | |
| thm_exponential_distribution_expectation_variance | ||
thm_exponential_distribution_expectation_variance (probability_theory/04_continuous_random_variables/0408_exponential_distribution) | theorem | |
| thm_joint_pmf_pdf | ||
thm_joint_pmf_pdf (probability_theory/05_joint_distributions/0501_joint_pmf_pdf/concept) | theorem | |
| thm_linear_transformation_gaussian_distribution | ||
thm_linear_transformation_gaussian_distribution (probability_theory/04_continuous_random_variables/0409_gaussian_distribution) | theorem | |
| thm_pdf_derivative_cdf | ||
thm_pdf_derivative_cdf (probability_theory/04_continuous_random_variables/0405_cumulative_distribution_function) | theorem | |
| thm_pmf_cdf | ||
thm_pmf_cdf (probability_theory/03_discrete_random_variables/0304_cumulative_distribution_function) | theorem | |
| thm_pmf_normalization | ||
thm_pmf_normalization (probability_theory/03_discrete_random_variables/0303_probability_mass_function) | theorem | |
| time-complexity | ||
time-complexity (dsa/searching_algorithms/binary_search/problems/875-koko-eating-bananas) | definition | |
| two-pointers-technique-algorithm | ||
two-pointers-technique-algorithm (dsa/two_pointers/two_pointers) | algorithm | |
| two-pointers-technique-meet-in-middle-algorithm | ||
two-pointers-technique-meet-in-middle-algorithm (dsa/two_pointers/two_pointers) | algorithm | |
| two-sum-167-two-sum-ii-input-array-is-sorted-two-pointers-algorithm | ||
two-sum-167-two-sum-ii-input-array-is-sorted-two-pointers-algorithm (dsa/two_pointers/questions/two_pointers/167-two-sum-ii-input-array-is-sorted) | algorithm | |
| two-sum-167-two-sum-ii-input-array-is-sorted-two-pointers-claim | ||
two-sum-167-two-sum-ii-input-array-is-sorted-two-pointers-claim (dsa/two_pointers/questions/two_pointers/167-two-sum-ii-input-array-is-sorted) | theorem | |
| two-sum-time-complexity-nested-loops-avg-case | ||
two-sum-time-complexity-nested-loops-avg-case (dsa/array/questions/01-two-sum) | remark | |
| type-theory-01-subtypes-definition-nominal-structural | ||
type-theory-01-subtypes-definition-nominal-structural (computer_science/type_theory/01-subtypes) | definition | |
| type-theory-01-subtypes-definition-subtype | ||
type-theory-01-subtypes-definition-subtype (computer_science/type_theory/01-subtypes) | definition | |
| type-theory-01-subtypes-example-int-type-as-set | ||
type-theory-01-subtypes-example-int-type-as-set (computer_science/type_theory/01-subtypes) | example | |
| type-theory-01-subtypes-remark-coercive-conversion | ||
type-theory-01-subtypes-remark-coercive-conversion (computer_science/type_theory/01-subtypes) | remark | |
| type-theory-04-generics-definition-type-constructor | ||
type-theory-04-generics-definition-type-constructor (computer_science/type_theory/04-generics) | definition | |
| type-theory-04-generics-remark-no-automatic-lifting | ||
type-theory-04-generics-remark-no-automatic-lifting (computer_science/type_theory/04-generics) | remark | |
| type-theory-06-variance-function-subtyping | ||
type-theory-06-variance-function-subtyping (computer_science/type_theory/06-invariance-covariance-contravariance) | theorem | |
| type-theory-liskov-substitution-principle | ||
type-theory-liskov-substitution-principle (computer_science/type_theory/03-subsumption) | theorem | |
| type-theory-subtype-and-type-safety | ||
type-theory-subtype-and-type-safety (computer_science/type_theory/02-type-safety) | definition | |
| type-theory-subtype-criterion | ||
type-theory-subtype-criterion (computer_science/type_theory/03-subsumption) | criterion | |
| underlying-distributions | ||
underlying-distributions (influential/naive_bayes/02_concept) | definition | |
| unordered-linear-search-mathematical-representation-iterative | ||
unordered-linear-search-mathematical-representation-iterative (dsa/searching_algorithms/linear_search/concept) | algorithm | |
| unordered-linear-search-pseudocode-iterative | ||
unordered-linear-search-pseudocode-iterative (dsa/searching_algorithms/linear_search/concept) | algorithm | |
| valid-parentheses-using-stack | ||
valid-parentheses-using-stack (dsa/stack/questions/20-valid-parentheses) | algorithm | |
| vc_dimension | ||
vc_dimension (influential/learning_theory/02_concept) | definition | |
| vc_dimension_of_a_2d_perceptron | ||
vc_dimension_of_a_2d_perceptron (influential/learning_theory/02_concept) | example | |
| vc_dimension_of_a_perceptron | ||
vc_dimension_of_a_perceptron (influential/learning_theory/02_concept) | theorem | |
| vc_generalization_bound | ||
vc_generalization_bound (influential/learning_theory/02_concept) | theorem | |
| why-do-we-use-warmup-cosine-scheduler-definition | ||
why-do-we-use-warmup-cosine-scheduler-definition (playbook/training/why_cosine_annealing_warmup_stabilize_training) | definition | |
| why-do-we-use-warmup-cosine-scheduler-definition-duplicate | ||
why-do-we-use-warmup-cosine-scheduler-definition-duplicate (influential/generative_pretrained_transformer/05_adder) | definition | |
| worst-case-only | ||
worst-case-only (dsa/stack/questions/232-implement-queue-using-stacks) | remark |